the weight W of an object varies inversly as the square of the distance d from the center of the earth at sea level (3979 m from the center of the earth), an astronaut weighs 136 lb. find her weight when she is 414 mi. above the surface of the earth and the space craft is not in motion. find her weight when she is 351 mi. above the surface of the earth and the spacecraft is not in motion.

Question

mathteacher1729 · Answer

Translation: 
Step 1: "The weight W of an object varies inversly as the square of the distance d from the center of the earth"

Step 2: Weight = some constant k times one over (distance) squared. 

Step 3 $$W = k \cdot 1/d^2$$

Now we want to figure out what the constant "k" is.  

Step 1 "at sea level (3979 m from the center of the earth), an astronaut weighs 136 lb."

Step 2 this means d = 3979 and W = 136  

Step 3 solve for k

$$136= k\cdot 1/(3979)^2$$

Hope this helps. :)